International audienceContext. The Galactic Cold Cores project has carried out Herschel photometric observations of 116 fields where the Planck survey has found signs of cold dust emission. The fields contain sources in different environments and different phases of star formation. Previous studies have revealed variations in their dust submillimetre opacity.Aims. The aim is to measure the value of dust opacity spectral index and to understand its variations spatially and with respect to other parameters, such as temperature, column density, and Galactic location.Methods. The dust opacity spectral index β and the dust colour temperature T are derived using Herschel and Planck data. The relation between β and T is examined for the whole samp...